Multistage identification of an N-L-N Hammerstein-Wiener system

In the paper we consider a problem of Hammerstein-Wiener (N-L-N) system identification in the presence of random input and random noise. The proposed strategy combines both parametric (e.g. least squares) and nonparametric (kernel) estimates (cf. [6]). First, the impulse response of the linear block, and the composition of two nonlinear characteristics are identified independently. Next, the nonlinear function composition is splited into two parts to obtain the models of all individual blocks of the system. The consistency of the proposed estimates is analyzed and simple simulation example is presented.